May 20

... start recording.

Looking ahead :

• Monday is our last class
  • It would be great to have as many of you do a brief presentation of your final project - share your screen, do a demo, explain what you did
  • Due date for the final version (code,docs,paper) is also Monday ... but up through the last day of classes (Thu) is OK.
  • Any questions about the final project and what's expected?
• Today ...
  • Part 1 : overview of what we've covered this semester.
  • Part 2 : time for an SEPC conversation (without me)

overview

"Algorithms" and "Data Structures"

algorithm

What is an "algorithm" ? A recipe for solving a math-ish problem, often of a certain size N

Big ideas :

• search : moving among "states" of the problem
• brute force : try every possible problem state
• divide and conquer : combine answer from same problem on half (usually) original
• greedy : move directly towards the solution (doesn't always give right answer)
• recursion : call the same function on a smaller part of the problem
• looping : the flip-side of recursion; often you can choose to do either
• dynamic programming : badly-named variation of divide-and-conquer; build up solution from smaller solutions in some order
• analysis of algorithms
  • time complexity - O() notation
    • O(1) : constant time
    • O( log(n) ) : fast
    • O( \( n^c \) ) for some constant c : polynomial ... not too bad
    • O( \( 2^n \) ) : exponential ... bad (brute force over all true/false for n variables)
    • O( n! ) : factorial ... really bad (brute force over all permutations)
  • space complexity - how much memory - same sort of ideas, but we didn't really cover
    • often there's a trade-off choice between optimizing for time or for space

data structure

What is a "data structure" ? A type of container to organize data, with an API of methods, and various O() behaviors

Algorithms use various data structures in their implementations .

For each of these, remind ourselves of the API and what they're used for.

• indexed array: stuff[i]
• linked list: a -> b -> c
• queue & stack
• hash table = dictionary
• priority queue = heap (well, often implemented as a heap anyway)
• tree : (a (b (c d) (e (f g))) ; nodes with children
• graph : vertices with neighbors ... in several flavors

We made the distinction between an "abstract data type" and an "implementation of an ADT".

python vs C

We used two languages this term, to at least some extent.

Pros and cons of each ?

problems

And we looked at a number of specific (and classic) problems, as illustrations of the big ideas. In some cases, we worked through several algorithms to solve the same problem.

• sorting
  • O( n! ) : bogosort
  • O( n**2 ) : bubble sort , for example
  • O( n * log(n) ) : quicksort , for example
  • O( n ) : bucket sort ... no comparisons ; only for limited types of data
• tree search
  • (depth or breadth) using (stack or queue)
  • recursive backtrack
  • maze generation & solution
  • peg solitarire solution
• graph
  • shortest path : Djikstra's , Floyd
  • min spanning tree : Prim's , Kruskal's
  • ... using dat structures like (priority queue + hash table)
• game search
  • min/max variation of tree search
  • variations : alpha-beta pruning ; iterative deepening
  • tic-tac-toe example

... and of course your own various final projects. ;)

life, the universe, and everything

Discussion of topics over the last week or so :

• complexity theory ... P vs NP
  • finite state machines, regular expressions
  • turing machines and what they can and can't do
• philosophy of mind ... is thinking computation?

coming attractions

CS courses for next year as currently scheduled :

Fall

• Coding Workshop (2 credits ; optional 3rd for individual project)
• Structure & Interpretation of Computer Programs
• Internet Seminar - various topics
• Tim : Python Programming

Spring

• Intro CS
• Algorithms
• Plan Programming Projects

... and we're planning on searching again for another CS faculty.

SEPC

Over to you ...